cp's OEIS Frontend

A047505 Numbers that are congruent to {0, 1, 2, 3, 6, 7} mod 8.

%I A047505 #15 Sep 08 2022 08:44:57
%S A047505 0,1,2,3,6,7,8,9,10,11,14,15,16,17,18,19,22,23,24,25,26,27,30,31,32,
%T A047505 33,34,35,38,39,40,41,42,43,46,47,48,49,50,51,54,55,56,57,58,59,62,63,
%U A047505 64,65,66,67,70,71,72,73,74,75,78,79,80,81,82,83,86,87,88
%N A047505 Numbers that are congruent to {0, 1, 2, 3, 6, 7} mod 8.
%H A047505 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1,-1).
%F A047505 G.f.: x^2*(1+x+x^2+3*x^3+x^4+x^5) / ( (1+x)*(x^2-x+1)*(1+x+x^2)*(x-1)^2 ). - _R. J. Mathar_, Nov 06 2015
%F A047505 From _Wesley Ivan Hurt_, Jun 16 2016: (Start)
%F A047505 a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.
%F A047505 a(n) = (24*n-27-3*cos(n*Pi)+12*cos(n*Pi/3)-4*sqrt(3)*sin(2*n*Pi/3))/18.
%F A047505 a(6k) = 8k-1, a(6k-1) = 8k-2, a(6k-2) = 8k-5, a(6k-3) = 8k-6, a(6k-4) = 8k-7, a(6k-5) = 8k-8. (End)
%F A047505 Sum_{n>=2} (-1)^n/a(n) = (sqrt(2)-1)*Pi/16 + (12-sqrt(2))*log(2)/16 + sqrt(2)*log(sqrt(2)+2)/8. - _Amiram Eldar_, Dec 26 2021
%p A047505 A047505:=n->(24*n-27-3*cos(n*Pi)+12*cos(n*Pi/3)-4*sqrt(3)*sin(2*n*Pi/3))/18: seq(A047505(n), n=1..100); # _Wesley Ivan Hurt_, Jun 16 2016
%t A047505 Select[Range[0, 100], MemberQ[{0, 1, 2, 3, 6, 7}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jun 16 2016 *)
%o A047505 (Magma) [n : n in [0..100] | n mod 8 in [0, 1, 2, 3, 6, 7]]; // _Wesley Ivan Hurt_, Jun 16 2016
%Y A047505 Cf. A047450, A047490.
%K A047505 nonn,easy
%O A047505 1,3
%A A047505 _N. J. A. Sloane_